Abstract
The main result of this paper is that every demonic refinement algebra with enabledness and termination is isomorphic to an algebra of ordered pairs of elements of a Kleene algebra with domain and with a divergence operator satisfying a mild condition. Divergence is an operator producing a test interpreted as the set of states from which nontermination may occur.
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References
Backhouse, R.: Galois connections and fixed point calculus. In: Backhouse, R., Crole, R.L., Gibbons, J. (eds.) Algebraic and Coalgebraic Methods in the Mathematics of Program Construction. LNCS, vol. 2297, pp. 89–150. Springer, Heidelberg (2002)
Berghammer, R., Zierer, H.: Relational algebraic semantics of deterministic and nondeterministic programs. Theoretical Computer Science 43(2–3), 123–147 (1986)
Cohen, E.: Separation and reduction. In: Backhouse, R., Oliveira, J.N. (eds.) MPC 2000. LNCS, vol. 1837, pp. 45–59. Springer, Heidelberg (2000)
De Carufel, J.L., Desharnais, J.: Demonic algebra with domain. Research report DIUL-RR-0601, Département d’informatique et de génie logiciel, Université Laval, Canada (June 2006), http://www.ift.ulaval.ca/~Desharnais/Recherche/RR/DIUL-RR-0601.pdf
De Carufel, J.L., Desharnais, J.: Demonic algebra with domain. In: Schmidt, R.A. (ed.) RelMiCS/AKA 2006. LNCS, vol. 4136, pp. 120–134. Springer, Heidelberg (2006)
De Carufel, J.L., Desharnais, J.: On the structure of demonic refinement algebras. Research report DIUL RR-0802, Département d’informatique et de génie logiciel, Université Laval, Québec, Canada (January 2008), http://www.ift.ulaval.ca/~Desharnais/Recherche/RR/DIUL-RR-0802.pdf
De Carufel, J.L., Desharnais, J.: Latest news about demonic algebra with domain. These proceedings
Desharnais, J., Möller, B., Struth, G.: Modal Kleene algebra and applications —A survey—. JoRMiCS — Journal on Relational Methods in Computer Science 1, 93–131 (2004)
Desharnais, J., Möller, B., Struth, G.: Kleene algebra with domain. ACM Transactions on Computational Logic (TOCL) 7(4), 798–833 (2006)
Desharnais, J., Möller, B., Struth, G.: Algebraic notions of termination. Research report 2006-23, Institut für Informatik, Universität Augsburg, Germany (October 2006)
Doornbos, H.: A relational model of programs without the restriction to Egli-Milner-monotone constructs. In: PROCOMET 1994: Proceedings of the IFIP TC2/WG2.1/WG2.2/WG2.3 Working Conference on Programming Concepts, Methods and Calculi, pp. 363–382. North-Holland, Amsterdam (1994)
Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press, Cambridge (2000)
Höfner, P., Möller, B., Solin, K.: Omega algebra, demonic refinement algebra and commands. In: Schmidt, R.A. (ed.) RelMiCS/AKA 2006. LNCS, vol. 4136, pp. 222–234. Springer, Heidelberg (2006)
Kozen, D.: A completeness theorem for Kleene algebras and the algebra of regular events. Information and Computation 110(2), 366–390 (1994)
Kozen, D.: Kleene algebra with tests. ACM Transactions on Programming Languages and Systems 19(3), 427–443 (1997)
Möller, B.: Kleene getting lazy. Science of Computer Programming 65, 195–214 (2007)
Möller, B., Struth, G.: wp is wlp. In: MacCaull, W., Winter, M., Düntsch, I. (eds.) RelMiCS 2005. LNCS, vol. 3929, pp. 200–211. Springer, Heidelberg (2006)
Parnas, D.L.: A generalized control structure and its formal definition. Communications of the ACM 26(8), 572–581 (1983)
Solin, K.: On two dually nondeterministic refinement algebras. In: Schmidt, R.A. (ed.) RelMiCS/AKA 2006. LNCS, vol. 4136, pp. 373–387. Springer, Heidelberg (2006)
Solin, K.: Abstract Algebra of Program Refinement. PhD thesis, Turku Center for Computer Science, University of Turku, Finland (2007)
Solin, K., von Wright, J.: Refinement algebra extended with operators for enabledness and termination. Technical Report 658, Turku Center for Computer Science, University of Turku, Finland, TUCS Technical Report (January 2005)
Solin, K., von Wright, J.: Refinement algebra with operators for enabledness and termination. In: Uustalu, T. (ed.) MPC 2006. LNCS, vol. 4014, pp. 397–415. Springer, Heidelberg (2006)
von Wright, J.: From Kleene algebra to refinement algebra. Technical Report 450, Turku Center for Computer Science (March 2002)
von Wright, J.: Towards a refinement algebra. Science of Computer Programming 51, 23–45 (2004)
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De Carufel, JL., Desharnais, J. (2008). On the Structure of Demonic Refinement Algebras with Enabledness and Termination. In: Berghammer, R., Möller, B., Struth, G. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2008. Lecture Notes in Computer Science, vol 4988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78913-0_7
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DOI: https://doi.org/10.1007/978-3-540-78913-0_7
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